Oryuin University Poker Department Entrance Exam

Exam proctor: Sigma (Twitter: @sigm_4)

Question 1

In the Nash equilibrium of the AKQ game defined below with a bet size of 500%, find how many times more QQ is included compared to AA in OOP's betting range.

[AKQ Game]
- The initial pot is 1. The bet size is 5.
- OOP holds AA and QQ each with 50% probability, and IP holds KK with 100% probability.
- OOP can choose to bet or check.
- IP can choose to call or fold against OOP's bet.
- If IP folds, OOP wins the entire pot at that point.
- If OOP checks, or if IP calls OOP's bet, a showdown occurs and the winner takes the entire pot. The showdown result is determined solely by the hand strength of each player's holdings.

Question 2

In the Nash equilibrium of the AQQ game defined below with a bet size of 500%, find how many times more QQ is included compared to AA in OOP's betting range.

[AQQ Game]
- The initial pot is 1. The bet size is 5.
- OOP holds AA with 1% probability and QQ with 99% probability, and IP holds QQ with 100% probability.
- OOP can choose to bet or check.
- IP can choose to call or fold against OOP's bet.
- If IP folds, OOP wins the entire pot at that point.
- If OOP checks, or if IP calls OOP's bet, a showdown occurs and the winner takes the entire pot. The showdown result is determined solely by the hand strength of each player's holdings.

Question 3

Consider the following situation.

On a K♤Q♤J♡T♢ board, OOP is about to go all-in for 500% pot. OOP's all-in range consists of A♤9♤ at a proportion of $x$ and A♡9♡ at a proportion of $1-x$, while IP always holds A♢9♢.

Find the value of $x$ that makes IP's A♢9♢ indifferent to OOP's all-in.

You may assume that the probability of a ♤ card appearing on the river is 2% per remaining ♤ card.

Question 4

Consider the following spot in a NL50 cash game with an effective stack of 100bb.

UTG vs. BB SRP
Preflop
    UTG: Raise 2.5bb
    BB: Call
Flop: K♤Q♤J♡ (Pot = 5.5bb)
    BB: Check
    UTG: Bet 1.8bb
    BB: Raise 6.35bb
    UTG: Call
Turn: T♢ (Pot = 18.2bb)
    BB: All-in
    UTG: ?

In Nash equilibrium, it is known that BB's all-in at this spot is performed only with A9s, and UTG does not call this all-in with anything other than A9s.

Estimate how many times more non-A♤9♤ suited A9s are included compared to A♤9♤ in BB's all-in range.

Answers

Oryuin University Poker Entrance Exam: Answer Key

Sigma Prep School: Sigma (Twitter: @sigm_4)

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